 In this problem, we have some data from a survey of students that go to Alabama or Auburn and they listed their preference of coaches, either Coach Saban or Coach Malzahn. We have this data and we want to do some analysis of conditional probabilities and find out does it matter the school whether or not you like Saban or Malzahn more. Intuitively you probably know the answer to that, but we're going to solve it using conditional probabilities. First thing you want to do is build a cross tablization or a contingency table. I'm going to click in the data, click on insert, pivot table, we want an existing worksheet, and I'm going to put it here and cell E and click OK. And we get some basic information there. I'm going to start by dragging school down into my rows, Coach preference into my columns, and then Coach preference into my values, and it comes up with the sums. And it shows we have 96 people responded to the survey, 35 from Alabama, 61 from Auburn. Let's convert that into percentages, which are the equivalent of probabilities. I'm going to click on the cell and go down here to value field settings. I'm going to click on show values as, change the calculation to percent of grand total and click OK. Now it shows percentages of the number of votes for Malzahn in this case by all of those folks is 9.38 percent of the total. We're going to change these into decimals by going to home, and I'm going to click on that to get to accounting and make it three decimal places. OK, now we want to fill out this table and it'll help us answer the question. And I'm just going to start by clicking in that cell and hit equal. And the probability of Auburn is the marginal probability there, Auburn row, the grand total is 0.635. Marginal probability of Alabama, of course, is that 0.365. I said 635365. Probability of Malzahn is the column total there, and similarly the probability of Saban is that column total. And we can go through here, the probability of Auburn and Saban is that cell, the intersection. The probability of Auburn and Malzahn is that intersection. The probability of Alabama and Saban, that cell, second. Probability of Alabama and Saban is that cell. And the probability of Alabama and Malzahn is that cell. And that fills out the top part of our table here. In the bottom I had pre-arranged some formulas there, and this is the the formula for calculating the R condition, Alabama R Saban. And that is just the probability of Auburn plus the probability of Saban minus the intersection, probability of Auburn and Saban. So that's K2, K4 minus K6. Two events are independent if the probability of A given B is equal to the probability of A. In this case, we could say the probability of Auburn given Saban is equal to the probability of Auburn. In other words, that Saban does not affect that probability. We can rearrange that and we can test to see if the probability of A and B, Auburn and Saban is equal to the probability of Auburn times the probability of Saban. And I've done it in this table here. Just copy down probability of Auburn's point 635. The probability of Saban also just happens to be point 635. The probability of Auburn and Saban is point 6365. The probability of Auburn times the probability of Saban is point 404. Since those two are not equal, we conclude that they are not independent. That whether or not you like Saban depends upon whether or not you went to Auburn or Alabama.